异质物体的分界面提取与边界面重构
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摘要
在体数据可视化中,等值面提取是一种物体表面重建技术。本质上,传统的等值面可以看作两类材质之间的分界面：标量值大于或小于特定值的两类材质。在现实世界中,很多物体包含了两类材质或者多类材质,即异质物体或多材质物体。对于每类材质,需要准确地确定其与其它材质之间的分界面,并高效地重建其与其它材质分离的边界曲面。而传统的等值面提取方法难以处理上述异质物体表示和建模问题。因此,研究高效、准确地重构异质物体中的分界面和边界面的方法和关键技术,既是对体数据可视化理论和方法的发展,同时在医学图像处理、异质物体建模等领域中具有重要的应用价值。
本文首先定量分析和对比了传统等值面提取算法。然后,针对定义在立方体单元上且已进行材质标注的体数据所表示的异质物体,分别提出了基于四面体单元和三棱柱单元的分界面提取方法和边界曲面重构方法,所得到的分界面和边界曲面均为2-流形,方便了后续的图形绘制和几何处理。此外,结合图形处理单元的强大并行计算能力对相关算法进行了加速。论文的主要工作包括：
等值面是曲面的一种分片线性逼近表示。为了定量表示逼近误差,引入了豪斯道夫距离、距离平均偏差、距离均方差等度量,并采用了多个具有不同次数和拓扑的代数曲面作为测试对象,定量地分析和对比了各种基于立方体和四面体单元的等值面提取算法的精度、效率和空间复杂度等,为实际应用中等值面提取算法的选取提供了指导。
提出了基于四面体单元的异质物体边界曲面重建算法,可以处理包含任意多类材质的异质物体。算法首先将立方体单元对称地剖分为六个四面体单元,然后根据四面体单元顶点的材质属性,生成将四面体完全分割成不同材质部分的三角面片,最后通过归类合并三角面片生成异质物体中所有物质的边界曲面。算法设计了层次数据结构用于表示异质物体中的边界曲面,并可以通过遍历数据结构高效地获取不同材质的边界面之间的各种相交信息,如分界面、交线等。此外,所有材质的边界曲面或不同材质之间的分界面均是2-流形。
通过发掘基于四面体单元的异质物体边界曲面重建算法的并行性,设计并实现了基于图形处理单元(GPU)和统一计算设备架构(CUDA)的加速算法。算法充分利用了GPU提供的强大数据收集与分散能力,以及对线程间数据访问具有加速作用的共享内存,并且将所生成的几何数据直接提供给图形流水线进行绘制,克服了大规模数据在显存和主存之间的传输瓶颈。
提出了基于三棱柱单元的异质物体边界曲面重建算法,大大降低了面片数量,提高了算法效率。算法首先将立方体单元对称地剖分为两个三棱柱单元,对三棱柱的每一个面和三棱柱本身进行”材质相关的序号编码”(MOIEM),然后以”维度攀升”的方式同时重建所有材质的边界曲面,即首先取三棱柱边与面上的分隔点,然后按规则连接分隔点生成分隔线,恰当遍历分割线依次生成环、分界面、边界面等。该算法同样不受材质种类数目的限制,而且算法的有效性和正确性可以通过MOIEM编码枚举的方式得以验证。
上述算法均已在统一的软件框架下实现,实验结果和分析证明了算法的有效性和正确性。本文研究为实现高效、准确的异质物体的边界表示和建模提供给了新的理论和方法,并将传统的体数据等值面提取算法推广至多材质分界面的情形,丰富和发展了科学数据可视化的理论和方法。论文在总结部分指出了进一步的研究方向。
Isosurface extraction is a fundamental technology in scientific data visualization. Es-sentially, an isosurface can be regarded as the interface between two materials, whose scalar value is greater or less than the specified value. In the real world, it is a common case that an object contains two or more than two materials, i.e., heterogeneous object or multi-material object. For each material in a heterogeneous object, it is necessary to accurately determine the interfaces between the material and the others in one pass, and efficiently reconstruct the boundary surface of the material. Obviously, the traditional isosurface extraction algo-rithms can not accomplish these goals. Thus, it is important to develop new methods for heterogeneous object representation and boundary surface reconstruction. The investiga-tion is an important extension to the isosurface extraction algorithms; meanwhile it can be potentially applied to medical image processing and heterogeneous object modeling;
In the thesis, the traditional isosurface extraction algorithms are first reviewed and compared quantitatively in detail. Then for the heterogeneous object defined on the cubi-cal voxels, the algorithms of interface extraction and boundary surface reconstruction are proposed, which are based on tetrahedral voxel and tri-prism voxel respectively. The inter-faces and boundary surfaces obtained are2-manifold, which is important for subsequent rendering and geometry processing. In addition, the massive parallel computing power of GPU is exploited to accelerate the algorithm. The main contributions of the thesis include:
Isosurface is a piecewisely linear approximation of the original surface. To quanti-tatively estimate the approximation errors of isosurfaces via different algorithms, several metrics are introduced, i.e., Hausdorff distance, mean deviation and mean square deviation. Five implicit surfaces of different degrees and topologies are employed to evaluate the ap-proximation accuracy, space complexity and time complexity of the most widely applied isosurface extraction algorithms, i.e., Marching Cubes algorithms and Marching Tetrahe- dra algorithms, respectively. The estimation results provide users a reference of selecting isosurface extraction algorithms.
A tetrahedron based boundary surface reconstruction algorithm is proposed for the heterogeneous objects. It is free of the number of materials in the heterogeneous object. As a pre-processing step, each cubical voxel is subdivided into6tetrahedral voxels. Accord-ing to the material types of tetrahedral vertices, the triangles are extracted to partition each heterogeneous tetrahedron into several homogeneous parts. Then, the boundary surface for each homogeneous material is generated by clustering the separating triangles prop-erly. A hierarchical data structure is carefully designed to organize the extracted surfaces so that the intersection information between or among the different materials can be re-trieved straightforwardly. Furthermore, the interfaces and boundary surfaces obtained are2-manifold.
The above tetrahedron based algorithm is accelerated using GPU and CUDA. The acceleration algorithm takes full advantages of the powerful gathering and scattering op-erations of GPU and the shared memory on-chip that can accelerate the data exchange between the working threads. The generated geometry data are sent into the rendering pipeline directly so that the huge data transfer bottleneck between main memory and the video memory is avoided.
To improve the reconstruction efficiency and reduce the triangle number in the bound-ary surfaces, a tri-prism based boundary surface reconstruction algorithm is proposed then. As a preprocessing step, each cubical voxel is subdivided into two tri-prism voxel. Then, each face in a tri-prism and each tri-prism are encoded by using Materials Oriented Index Encoding Method (MOIEM). The boundary surfaces of the heterogeneous object are re-constructed in a dimension-ascending (DA) way, i.e., first extracting the separating points on the edges or in the faces of the tri-prism, then generating the separating line segments by connecting the separating points, and finally generating the loops, interfaces, boundary surfaces. The tri-prism based reconstruction algorithm is also independent of the number of material types in the heterogeneous object. The validation and correctness can be verified using MOIEM in an enumeratedly way.
The algorithms mentioned above has been implemented and integrated into a hetero-geneous object reconstruction system. The experimental results show the validation and correctness of the proposed algorithms. The above methods provide new approaches of the heterogeneous object representation and modeling. They also extend the isosurface extrac-tion algorithms to the heterogeneous case, subsequently enrich the theoretical framework and related technologies in the area of scientific data visualization. Finally, the future works are indicated in the conclusion section.
本文首先定量分析和对比了传统等值面提取算法。然后,针对定义在立方体单元上且已进行材质标注的体数据所表示的异质物体,分别提出了基于四面体单元和三棱柱单元的分界面提取方法和边界曲面重构方法,所得到的分界面和边界曲面均为2-流形,方便了后续的图形绘制和几何处理。此外,结合图形处理单元的强大并行计算能力对相关算法进行了加速。论文的主要工作包括：
等值面是曲面的一种分片线性逼近表示。为了定量表示逼近误差,引入了豪斯道夫距离、距离平均偏差、距离均方差等度量,并采用了多个具有不同次数和拓扑的代数曲面作为测试对象,定量地分析和对比了各种基于立方体和四面体单元的等值面提取算法的精度、效率和空间复杂度等,为实际应用中等值面提取算法的选取提供了指导。
提出了基于四面体单元的异质物体边界曲面重建算法,可以处理包含任意多类材质的异质物体。算法首先将立方体单元对称地剖分为六个四面体单元,然后根据四面体单元顶点的材质属性,生成将四面体完全分割成不同材质部分的三角面片,最后通过归类合并三角面片生成异质物体中所有物质的边界曲面。算法设计了层次数据结构用于表示异质物体中的边界曲面,并可以通过遍历数据结构高效地获取不同材质的边界面之间的各种相交信息,如分界面、交线等。此外,所有材质的边界曲面或不同材质之间的分界面均是2-流形。
通过发掘基于四面体单元的异质物体边界曲面重建算法的并行性,设计并实现了基于图形处理单元(GPU)和统一计算设备架构(CUDA)的加速算法。算法充分利用了GPU提供的强大数据收集与分散能力,以及对线程间数据访问具有加速作用的共享内存,并且将所生成的几何数据直接提供给图形流水线进行绘制,克服了大规模数据在显存和主存之间的传输瓶颈。
提出了基于三棱柱单元的异质物体边界曲面重建算法,大大降低了面片数量,提高了算法效率。算法首先将立方体单元对称地剖分为两个三棱柱单元,对三棱柱的每一个面和三棱柱本身进行”材质相关的序号编码”(MOIEM),然后以”维度攀升”的方式同时重建所有材质的边界曲面,即首先取三棱柱边与面上的分隔点,然后按规则连接分隔点生成分隔线,恰当遍历分割线依次生成环、分界面、边界面等。该算法同样不受材质种类数目的限制,而且算法的有效性和正确性可以通过MOIEM编码枚举的方式得以验证。
上述算法均已在统一的软件框架下实现,实验结果和分析证明了算法的有效性和正确性。本文研究为实现高效、准确的异质物体的边界表示和建模提供给了新的理论和方法,并将传统的体数据等值面提取算法推广至多材质分界面的情形,丰富和发展了科学数据可视化的理论和方法。论文在总结部分指出了进一步的研究方向。
Isosurface extraction is a fundamental technology in scientific data visualization. Es-sentially, an isosurface can be regarded as the interface between two materials, whose scalar value is greater or less than the specified value. In the real world, it is a common case that an object contains two or more than two materials, i.e., heterogeneous object or multi-material object. For each material in a heterogeneous object, it is necessary to accurately determine the interfaces between the material and the others in one pass, and efficiently reconstruct the boundary surface of the material. Obviously, the traditional isosurface extraction algo-rithms can not accomplish these goals. Thus, it is important to develop new methods for heterogeneous object representation and boundary surface reconstruction. The investiga-tion is an important extension to the isosurface extraction algorithms; meanwhile it can be potentially applied to medical image processing and heterogeneous object modeling;
In the thesis, the traditional isosurface extraction algorithms are first reviewed and compared quantitatively in detail. Then for the heterogeneous object defined on the cubi-cal voxels, the algorithms of interface extraction and boundary surface reconstruction are proposed, which are based on tetrahedral voxel and tri-prism voxel respectively. The inter-faces and boundary surfaces obtained are2-manifold, which is important for subsequent rendering and geometry processing. In addition, the massive parallel computing power of GPU is exploited to accelerate the algorithm. The main contributions of the thesis include:
Isosurface is a piecewisely linear approximation of the original surface. To quanti-tatively estimate the approximation errors of isosurfaces via different algorithms, several metrics are introduced, i.e., Hausdorff distance, mean deviation and mean square deviation. Five implicit surfaces of different degrees and topologies are employed to evaluate the ap-proximation accuracy, space complexity and time complexity of the most widely applied isosurface extraction algorithms, i.e., Marching Cubes algorithms and Marching Tetrahe- dra algorithms, respectively. The estimation results provide users a reference of selecting isosurface extraction algorithms.
A tetrahedron based boundary surface reconstruction algorithm is proposed for the heterogeneous objects. It is free of the number of materials in the heterogeneous object. As a pre-processing step, each cubical voxel is subdivided into6tetrahedral voxels. Accord-ing to the material types of tetrahedral vertices, the triangles are extracted to partition each heterogeneous tetrahedron into several homogeneous parts. Then, the boundary surface for each homogeneous material is generated by clustering the separating triangles prop-erly. A hierarchical data structure is carefully designed to organize the extracted surfaces so that the intersection information between or among the different materials can be re-trieved straightforwardly. Furthermore, the interfaces and boundary surfaces obtained are2-manifold.
The above tetrahedron based algorithm is accelerated using GPU and CUDA. The acceleration algorithm takes full advantages of the powerful gathering and scattering op-erations of GPU and the shared memory on-chip that can accelerate the data exchange between the working threads. The generated geometry data are sent into the rendering pipeline directly so that the huge data transfer bottleneck between main memory and the video memory is avoided.
To improve the reconstruction efficiency and reduce the triangle number in the bound-ary surfaces, a tri-prism based boundary surface reconstruction algorithm is proposed then. As a preprocessing step, each cubical voxel is subdivided into two tri-prism voxel. Then, each face in a tri-prism and each tri-prism are encoded by using Materials Oriented Index Encoding Method (MOIEM). The boundary surfaces of the heterogeneous object are re-constructed in a dimension-ascending (DA) way, i.e., first extracting the separating points on the edges or in the faces of the tri-prism, then generating the separating line segments by connecting the separating points, and finally generating the loops, interfaces, boundary surfaces. The tri-prism based reconstruction algorithm is also independent of the number of material types in the heterogeneous object. The validation and correctness can be verified using MOIEM in an enumeratedly way.
The algorithms mentioned above has been implemented and integrated into a hetero-geneous object reconstruction system. The experimental results show the validation and correctness of the proposed algorithms. The above methods provide new approaches of the heterogeneous object representation and modeling. They also extend the isosurface extrac-tion algorithms to the heterogeneous case, subsequently enrich the theoretical framework and related technologies in the area of scientific data visualization. Finally, the future works are indicated in the conclusion section.
引文
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